Introduction to Types of Graphs—Vertical Bar Graphs, Horizontal Bar Graphs, and Histograms
When the variables in a function can attain only a few values (called discrete values ), graphs can be rendered in simplified forms. Here are some of the most common types.
Vertical Bar Graphs
In a vertical bar graph , the independent variable is shown on the horizontal axis and the dependent variable is shown on the vertical axis. Function values are portrayed as the heights of bars having equal widths. Figure 24 is a vertical bar graph of the price of the hypothetical Stock Y at intervals of 1 hour.
Fig. 24. Vertical bar graph of hypothetical stock price versus time.
Horizontal Bar Graphs
In a horizontal bar graph , the independent variable is shown on the vertical axis and the dependent variable is shown on the horizontal axis. Function values are portrayed as the widths of bars having equal heights. Figure 25 is a horizontal bar graph of the price of the hypothetical Stock Y at intervals of 1 hour. This type of graph is used much less often than the vertical bar graph. This is because it is customary to place the independent variable on the horizontal axis and the dependent variable on the vertical axis in any graph, when possible.
Fig. 25. Horizontal bar graph of hypothetical stock price versus time.
Histograms
A histogram is a bar graph applied to a special situation called a distribution . An example is a portrayal of the grades a class receives on a test, such as is shown in Fig. 26. Here, each vertical bar represents a letter grade (A, B, C, D, or F). The height of the bar represents the percentage of students in the class receiving that grade.
Fig. 26. A histogram is a bar graph that shows a statistical distribution.
In Fig. 26, the values of the dependent variable are written at the top of each bar. In this case, the percentages add up to 100%, based on the assumption that all of the people in the class are present, take the test, and turn in their papers. The values of the dependent variable are annotated this way in some bar graphs. It’s a good idea to write in these numbers if there aren’t too many bars in the graph, but it can make the graph look messy or confusing if there are a lot of bars.
In some bar graphs showing percentages, the values do not add up to 100%. We’ll see an example of this shortly.
Other Types of Simple Graphs—Nomographs and Line Graphs
Nomographs
A nomograph is a onedimensional graph that consists of two graduated scales lined up directly with each other. Such graphs are useful when the magnitude of a specific quantity must be compared according to two different unit scales. In Fig. 27, a nomograph compares temperature readings in degrees Celsius (also called centigrade) and degrees Fahrenheit.
Fig. 27. An example of a nomograph for converting temperature readings.
PointToPoint Graphs
In a pointtopoint graph , the scales are similar to those used in continuouscurve graphs such as Figs. 22 and 23. But the values of the function in a pointtopoint graph are shown only for a few selected points, which are connected by straight lines.
In the pointtopoint graph of Fig. 28, the price of Stock Y (from Fig. 22) is plotted on the halfhour from 10:00 A.M. to 3:00 P.M. The resulting “curve” does not exactly show the stock prices at the inbetween times. But overall, the graph is a fair representation of the fluctuation of the stock over time.
When plotting a pointtopoint graph, a certain minimum number of points must be plotted, and they must all be sufficiently close together. If a pointtopoint graph showed the price of Stock Y at hourly intervals, it would not come as close as Fig. 28 to representing the actual momenttomoment stockprice function. If a pointtopoint graph showed the price at 15minute intervals, it would come closer than Fig. 28 to the momenttomoment stockprice function.
Fig. 28. A pointtopoint graph of hypothetical stock price versus time.

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